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\begin{document}

\title{\vspace{-6ex}\textbf{Does the US have an Infrastructure Cost Problem? Evidence from the Interstate Highway System}\thanks{We are grateful to Julia Lynn and Margaux Kelley for excellent research assistance and to Patrick McCarthy for helpful comments. We are also grateful for financial support from the National Science Foundation program on `Economics of Transportation in the 21st Century', and Turner gratefully acknowledges the support of a Kenen Fellowship at Princeton University during part of the time this research was conducted.}}
\author{
Neil Mehrotra,\thanks{Federal Reserve Bank of Minneapolis, 90 Hennepin Avenue, \textsc{mn} 55401. email: \texttt{neil.mehrotra@mpls.frb.org}.} 
%
~Matthew A. Turner,\thanks{Department of Economics, Box B, Brown University, Providence, \textsc{ri} 02912. email: \texttt{matthew\_turner@brown.edu}. Also affiliated with PERC, IGC, NBER, PSTC, and S4.}
%
~Juan Pablo Uribe\thanks{Cornerstone Research, 699 Boylston Street, 5th Floor, Boston, MA 02116 email: \texttt{jp.uribe86@gmail.com.}}
}
\date{\today}

\maketitle
\thispagestyle{empty}

%\baselineskip=18pt
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\section{Main Figures and Tables}

%%FIGURE 1
\begin{figure}[t]
\caption{Trends in the state of the Interstate highway system}
\label{fig:background}
\centering
\begin{tabular}{cccc}
\includegraphics[width=2.6in]{figures/Figure1_lane_miles_IH.pdf} &
\includegraphics[width=2.6in]{figures/Figure1_iri_IHnat.pdf}\\[-1ex]
   (a) lane miles/1,000 &(b) \textsc{iri} \\
\includegraphics[width=2.6in]{figures/Figure1_IH_expenditure.pdf}&
\includegraphics[width=2.6in]{figures/Figure1_aadt_IH.pdf}\\[-1ex]
(c) Expenditure/$10^9$&(d) \textsc{aadt}/10,000\\
\end{tabular}
\flushleft
\emph{Note}: (a) Total Interstate lane miles by year ('000 miles). (b) Lane mile weighted \textsc{iri}  for the whole Interstate by year, (inches per mile). (c) Total Interstate expenditure by year and category. Dark gray is construction, medium gray is resurfacing, light gray is maintenance ($10^9$ 2010\textsc{usd}). (d) Lane mile weighted \textsc{aadt} for the whole Interstate by year (vehicles/day). (a), (b) and the solid line in (d) are based on the \textsc{hpms} Universe Data. The dashed line in figure (d) is based on the \textsc{hpms} Sample Data. (c) is based on Highway Statistics.
\end{figure}

%%Table 1: 
\input{tables/Table1_Trends_table.tex}


%%Figure 2
\begin{figure}[t]
\centering
\caption{Effect of resurfacing expenditure on \textsc{iri}  by year}
\label{fig:resurfacing}
\begin{tabular}{c}
\includegraphics[width=2.5in]{figures/Figure2_year_X_I2exp_1_linear.pdf}\\
\end{tabular}
\flushleft
\emph{Note}: x-axis is years, y-axis is inches per resurfaced mile from one million dollars per resurfaced mile of resurfacing expenditure. The solid line plots the trend in change in \textsc{iri} and millions of dollars of expenditure per lane mile between 1992 and 2008 estimated in column 6 of table \ref{tab:IRI_expenditure}. This plot is the basis for the time series of $p^q$ that we use in our calibration exercise in section \ref{sec:calibration} and report in table \ref{tab:national_vars}.
\end{figure}

% Table 2


\input{tables/Table2_sample_regressions}


% Table 3

\input{tables/Table3_universe_regressions}


%Figure 3
\begin{figure}[h]
\centering
\caption{Effect of construction expenditure on lane miles by year}
\label{fig:construction}
\begin{tabular}{c}
\includegraphics[width=2.5in]{figures/Figure3_yearXexpL_0_linear.pdf}\\
\end{tabular}
\flushleft
\emph{Note}: x-axis is years, y-axis is lane kilometers per million dollars. 95\%CI's based on robust standard errors. The solid line plots the trend in lane miles per million dollars between 1992 and 2008 estimated in column 4 of table \ref{tab:DL_regs1}. This plot is the basis for the time series of $p^L$ that we use in our calibration exercise in section \ref{sec:calibration} and report in table \ref{tab:national_vars}.
\end{figure}




%Table 4
\input{tables/Table4_sample_composition}


%Figure 4
\begin{figure}[t]
\centering
\caption{Inverse price of asphaltic concrete over time}
%\label{fig:SN_event_study}
\label{fig:asphalt_time_series}
\begin{tabular}{c}
\includegraphics[width=2.5in]{figures/Figure4_Bituminousconcrete_plm_inv.pdf}\\[-1.2ex]
\end{tabular}
\flushleft
\emph{Note}: Minus one times lane miles worth of asphaltic concrete per million \textsc{usd}2010 of expenditure, assuming a one inch thick resurfacing layer.
\end{figure}


%Figure 5 
\begin{figure}[t]
\caption{Steady state user cost per vehicle mile travelled over time}
\centering
\label{fig:ss_foc}
\begin{tabular}{c}
\includegraphics[width=2.5in]{figures/Figure5_opt_mtn_RHS_92_08.pdf} \\
\end{tabular}
\flushleft
\emph{Note}:  User cost of Interstate capital per vehicle mile implied by steady state condition \eqref{eq:ss_equil}. Figure based  on data in table \ref{tab:national_vars}.   
\end{figure}

%Table 5
\input{tables/Table5}


\begin{figure}[t]
\caption{Observed user cost per mile based on federal gas tax.}
\centering
\label{fig:gas_tax}
\begin{tabular}{c}
\includegraphics[width=2.5in]{figures/Figure6_opt_mtn_LHS.pdf}\\[-2ex]
\\
\end{tabular}
\flushleft
\emph{Note}: User cost per mile in 2010USD based on federal gas tax.  This user cost is calculated from the annual total of all user fees and taxes (mainly gas tax revenue) from Highway Statistics Table \textsc{fe}9. We discount this sum by the fraction of all \textsc{vmt} carried by the Interstate as calculated from the Sample Data. To arrive at a per user mile value, we divide by total annual Interstate \textsc{vmt}.
\end{figure}

\newpage
\section{Appendix}
\appendix
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\label{app:data}


\input{tables/TableA1_Data_Appendix}



\input{tables/TableA2_Data_Appendix_missing_sample}




 \begin{figure}[h]
\centering
\caption{Comparing PR511 and \textsc{hpms} aggregate mileage}
\label{fig:BL_vs_MTU}
\begin{tabular}{c}
 \includegraphics[width=2.9in]{figures/FigureA1_compare_MTU_BL.pdf}
\end{tabular}
\flushleft
\emph{Note}: Light gray dashed line is total miles of Interstate by year from the PR511 data on which \cite{Brooks_Liscow_AEJ_2023} is based. Medium gray line is corresponding quality from the \textsc{hpms} data on which this paper is based. Black line in lane miles of Interstate from the \textsc{hpms}.  All three series are normalized to 1 in 1984, the first year we study. We see that the two mileage estimates track each other closely. Lane miles, however, grow more quickly.
\end{figure}


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\begin{figure}[h]
\caption{Effect of resurfacing on \textsc{iri}  by year}
\centering
\label{fig_app:resurfacing}
\begin{tabular}{c}
\includegraphics[width=2.5in]{figures/FigureB1_year_X_I2_1.pdf}
\end{tabular}
\flushleft
\emph{Note}: x-axis is years, y-axis is inches. This figure reports the results of an estimation of equation \eqref{eq:resurfacing_by_year} and illustrates the effect of resurfacing on the \textsc{iri}  of resurfaced segments. The figure shows a barely discernible trend upwards, so that a resurfacing event leads to a marginally smaller reduction in \textsc{iri}  at the end of the sample than the beginning. 
\end{figure}

\input{tables/TableB1_sample_regressions1_I2_t_SEstate_year}


\input{tables/TableB1_sample_regressions1_I2_t_SEstate_year}

\begin{figure}[t]
\centering
\caption{Event Study of Structural Number and \textsc{iri} }
\label{fig:SN_event_study}
\begin{tabular}{c}
\includegraphics[width=2.5in]{figures/FigureB2_events.pdf}\\[-1.2ex]
\end{tabular}
\flushleft
\emph{Note}: Changes in \textsc{iri}  and structural number around resurfacing events for all segments with flexible pavement. 
\end{figure}
There are 2552 segments for which we observe a resurfacing event and also observe the segment for at least two years before and after resurfacing. Of these, 926 have flexible pavement. Figure \ref{fig:SN_event_study} presents the results from the event study showing how structural number changes around resurfacing events for these 926 segments.  For reference, the figure also shows the corresponding event study for \textsc{iri}. Except for the different sample, the about 25 inch drop in \textsc{iri}  around resurfacing that we see in figure \ref{fig:SN_event_study} is comparable to the within segment estimate in table \ref{tab:IRI_resurfacing} column (6). Note that we can use this same research design to check  whether the change in structural number from resurfacing is constant throughout our sample. The data do not indicate that the amount of paving material used for resurfacing changes over our study period.

\input{tables/TableB2_universe_regressions}

\input{tables/TableB3_universe_comp}
%S:\Construction\data_processing\analysis\draft\sample_regressions1_I2_v2.do
\begin{figure}[t]
\caption{Millions of dollars per mile of Interstate maintenance expenditure by year.}
\centering
\label{fig_app:maintenance}
\begin{tabular}{c}
\includegraphics[width=3.85in]{figures/FigureB3_maint.pdf}\\[-4ex]
\end{tabular}
\flushleft
\emph{Note}: Plot of average state maintenance expenditure per lane-mile over time.
\end{figure}

\begin{figure}
\caption{Risk free interest rate}
   \label{fig:r_linear}
    \centering
    \includegraphics[width=3.85in]{figures/FigureB4_i_rate.pdf}\\
    \flushleft
     \emph{Note}: Dots indicate January average of the 10 year Treasury rate net of the annual inflation rate calculated from the \textsc{cpi}. Solid line is a local linear regression. Dotted line is the best linear approximation that yields the values of $r_t$ that we use in our calibrations exercise and report in table \ref{tab:national_vars}. 
\end{figure}



\begin{figure}
\caption{Estimates of lane miles per million dollars of expenditure and of $p^L$}
\label{fig:p_l_robustness}
\begin{tabular}{ccc}
    \centering
    \includegraphics[width=2.85in]{figures/FigureB5_P_const.pdf}&
    \includegraphics[width=2.85in]{figures/FigureB5_p_L.pdf}\\
    (a) & (b)\\
\end{tabular}
\flushleft
\emph{Note}: Panel (a) plots the different regressions that we use to estimate $p^L$. Dots reproduce mean miles of new construction per million dollars by year from figure \ref{fig:resurfacing}.  The dashed black line  is based on column 3 and is used in our baseline calibration exercise. The solid black linear fit is based on column 2. The heavy black non-linear curve is constructed by applying LOWESS to to annual means, i.e., the dots in the figure. The green line is based on a replication of column 3 of table \ref{tab:DL_regs1} (not shown) but instruments for expenditure using lagged appropriations. Panel (b) presents identical information as in panel (a) but transforms regression estimates of lane miles per million dollars of expenditure into prices, millions of dollars per lane-mile by year, using the transformation described in the text. The dashed black line in (b) matches the values of $p^L$ that we report in table \ref{tab:national_vars} and use in our baseline calibration.  
\end{figure}



\newcommand{\noteTableVars}{\emph{Note}: Annual values of all variable used in calibration exercise of section \ref{sec:calibration}. $L$ is total lane miles. $q$ is system average \textsc{iri}. $\tau^{\text{gas}}$ is actual gas tax revenue per vehicle mile and reported in figure \ref{fig:gas_tax}. $r$ is the real interest rate. $p^L$ is millions of 2010\textsc{usd} per lane-mile. $p^q$ is inches of roughness eliminated per million dollars of 2010\textsc{usd} expenditure. $m$ is non-resurfacing maintenance expenditure per Interstate vehicle mile travelled.}

\input{tables/TableB5_national_variables.tex}

\begin{figure}[th]
\caption{User cost per vehicle mile travelled over time}
\centering
\label{fig:euler_foc}
\begin{tabular}{ccc}
\includegraphics[width=2.5in]{figures/FigureB6_r_h_L_alphas_all_92_08.pdf}&
\includegraphics[width=2.5in]{figures/FigureB6_r_h_q_alphas_92_08.pdf}\\
(a) eq \eqref{eq:euler_calibration_a} & (b) eq \eqref{eq:euler_calibration_b} \\[0ex]
\end{tabular}
\flushleft
\emph{Note}: (a) User cost of Interstate capital per vehicle mile implied by Euler condition \eqref{eq:euler_calibration_a} (b)  User cost of Interstate capital per vehicle mile implied by Euler condition \eqref{eq:euler_calibration_b}.  All figures rely on the data in table \ref{tab:national_vars}. In both panels the solid black line indicates calibration to actual data with $\alpha=0.1$; dashed grey line is $\alpha=0.4$.   
\end{figure}


\end{document}
